Graduate Courses 2023-2024
The class schedule is subject to change at any time. Such changes are not always reflected immediately on this page. Please check classes.uoregon.edu for the accurate, live schedule for the term.
All the other courses are described in the University of Oregon Catalog. To view graduate courses offered in previous years, please visit the Graduate Course History page.
On this page:
Schedule | Math Course Descriptions
Schedule
| FALL 2023 | WINTER 2024 | SPRING 2024 |
| 513 Intro to Analysis I Addington, N 9:00 – 9:50 MWF |
514 Intro to Analysis II Xu, Y 9:00 – 9:50 MWF |
515 Intro to Analysis III He, W 9:00 – 9:50 MWF |
| 532 Intro to Topology II Hersh, P 1200-12:50 MWF |
||
| 544 Intro to Abstract Algebra I Elias, B 14:00 – 14:50 MWF |
545 Intro to Abstract Algebra II Elias, B 14:00 – 14:50 MWF |
546 Intro to Abstract Algebra III Eischen, E 14:00 – 14:50 MWF |
| 607 Introduction to Optimal Transport Theory and Applications Warren, M 10:00 – 11:20 TR |
607 Tensor categories Ostrik, V 14:00 – 15:20 TR |
607 Topological combinatorics Hersh, P 10:00 – 11:20 TR |
| 607 Applied Math I: Physics-informed machine learning Erickson, B 12:00 – 13:20 TR |
607 Applied Math II: Statistical learning Murray, J 12:00 – 13:20 TR |
607 Applied Math III: Applied stochastic processes Ralph, P 12:00 – 13:20 TR |
| 607 Algebraic number theory Eischen, E 12:00 – 13:20 MW |
607 Integrable Algebraic Combinatorics Young, B 13:00 – 13:50 MWF |
607 Categorical representation theory Elias, B 12:00 – 12:50 MWF |
| 616 Real Analysis Lin, H 9:00 – 9:50 MWF |
617 Real Analysis Phillips, C 9:00 – 9:50 MWF |
618 Real Analysis Phillips, C 9:00 – 9:50 MWF |
| 634 Algebraic Topology Shen, Y 11:00 – 11:50 MWF |
635 Algebraic Topology Liphitz, R 11:00 – 11:50 MWF |
636 Algebraic Topology Liphitz, R 11:00 – 11:50 MWF |
| 637 Differential Geometry He, W 10:00 – 10:50 MWF |
638 Differential Geometry Warren, M 10:00 – 10:50 MWF |
639 Differential Geometry Warren, M 10:00 – 10:50 MWF |
| 647 Abstract Algebra Brundan, J 15:00 – 15:50 MWF |
648 Abstract Algebra Kleshchev, A 15:00 – 15:50 MWF |
649 Abstract Algebra Elias, B 15:00 – 15:50 MWF |
| 681 Algebraic geometry I Polishchuk, A 14:00 – 14:50 MWF |
682 Algebraic geometry II Polishchuk, A 14:00 – 14:50 MWF |
683 Algebraic geometry III Addington, N 14:00 – 14:50 MWF |
| 684 Functional Analysis–Introduction to Operator Algebras Lin, H 10:00 – 10:50 MWF |
685 Group C*-algebras and crossed products Phillips, C 12:00-12:50 MWF |
686 The Cuntz semigroup of a C*-algebra Phillips, C 12:00-12:50 MWF |
| 690 Morse Theory Dugger, D 12:00 – 12:50 MWF |
691 Spectral Sequences Botvinnik, B 11:00-11:50 MWF |
692 Introduction to low-dimensional topology Lipshitz, R 12:00-12:50 MWF |
Math Course Descriptions
Math 607 Applied Math I: Physics-informed machine learning
Fall 2023
Instructor: Brittany Erickson
This course will cover fundamentals of both traditional numerical (e.g. finite difference) and deep learning (DL) approaches for solving partial differential equations (PDE), exploring the pros and cons of each approach. We will review traditional methods, which have seen incredible growth in the past century, but whose integration with noisy or sparse data is currently limited. Machine learning (ML), on the other hand, excels in the presence of large data and despite being an actively growing field, does not always incorporate rigorous physics. We will focus on the Physics-Informed Neural Network (PINN), which seamlessly integrates sparse and/or noisy data while ensuring that model outcomes satisfy rigorous physical constraints. Students will gain knowledge of PDE and associated numerical methods while advancing their skills in Python programming.
Math 607 Introduction to Optimal Transport Theory and Applications
Fall 2023
Instructor: Micah Warren
Optimal transport is a branch of mathematics that studies the problem of efficiently moving one mass distribution (e.g., a pile of dirt) to another (e.g., a hole) while minimizing the cost of transport (e.g., the amount of effort required to move the dirt). This course will provide a comprehensive introduction to the theory and applications of optimal transport.
Topics to be covered include:
-The Monge-Kantorovich problem, which is the classical formulation of the optimal transport problem
-The duality theory of optimal transport, which relates the primal optimal transport problem to a dual problem involving convex optimization
-The theory of optimal transport maps, including the existence and regularity of such maps
-Applications of optimal transport in machine learning, including the use of optimal transport to define distances between probability distributions, giving us the Wasserstein metric
-Examine the use of optimal transport in the study of partial differential equations and geometry, including the concept of Ricci curvature
Prerequisites for this course include a foundation in real analysis and basic probability theory.
Math 607 Applied Math II: Statistical learning
Winter 2024
Instructor: James Murray
This course covers statistical and machine learning theory using foundational approaches. Topics include probability theory, regression, classification, kernel methods, mixture models, and expectation maximization, as well as inference for sequential data using hidden Markov models and linear dynamical systems.
Math 607 Categorical representation theory
Spring 2024
Instructor: Ben Elias
This course will give an introduction to categorical representation theory, with a focus on the Hecke category. In type A, this is a categorification of the group algebra of the symmetric group, or its q-deformation, the Iwahori-Hecke algebra. We will introduce concepts like: the Kazhdan-Lusztig basis, Soergel bimodules, Soergel diagrammatics, Specht modules, cell theory, categorical representations, categorical diagonalization. Exact topics covered will depend on time and student interest.
Math 607: Topological combinatorics
Winter 2023
Instructor: Patricia Hersh
A main focus in this class will be topological-combinatorial techniques such as shellability, discrete Morse theory, and the Quillen Fiber Lemma. We will discuss how these may be used to prove abstract simplicial complexes are homotopy equivalent to wedges of spheres (in some cases), for upper bounding Betti numbers (in other cases) and calculating Euler characteristic (in still other cases). We will also discuss enrichments of this story, in particular group actions on posets and consequent group representations on poset homology. All of these methods will be applied to quite down-to-earth examples including various poset order complexes, as well as other combinatorial simplicial complexes such as Coxeter complexes and chessboard complexes. As time permits and depending on the interests of the students, we will also discuss one or more quite surprising applications to other areas such as complexity theory, graph theory, combinatorial algebraic geometry and commutative algebra. While some familiarity with partially ordered sets will be helpful, it will not be required as a prerequisite. As textbook for this course, we will use the freely available chapter by Michelle Wachs called “Poset topology: tools and applications” along with survey articles of Bjoerner, Forman, and Stanley.
Math 684: Functional Analysis–Introduction to Operator Algebras
Fall 2023
Instructor: Huaxin Lin
We will introduce some basics of operator algebras, such as spectral theorem, commutative and non-commutative C*-algebras. We will also discuss inductive limit of C*-algebras as well as C*-algebras from dynamical systems. There will be no exams.
Math 685: Group C*-algebras and crossed products
Winter 2024
Instructor: N. Christopher Phillips
The material can be modified depending on the interests of the
students.
For a locally compact group G, the group C*-algebra C* (G) plays the same role for unitary representations of G on Hilbert spaces that the group ring in algebra plays for arbitrary representations on vector spaces over a field. The crossed product is a generalization, incorporating an action of the group on another C*-algebra. It also has an algebraic counterpart, the skew group ring. Group C*-algebras and crossed products are among the most intensively studied C*-algebras, and many of the most important examples can be realized as crossed products.
In this course, we will follow up on the introduction of this topic in Math 684, and, for example, study their ideal structure, structural properties such as stable and real rank, and their K-theory. (K-theory of general C*-algebras will be treated in Math 684.) We will concentrate on discrete groups, where more is known and where the proofs are easier. There will be many pointers to interesting material for which there isn’t time in the course for a careful treatment, including analogs for other kinds of Banach algebras.
There will be no exams in this course.
Math 686, The Cuntz semigroup of a C*-algebra
Spring 2024
Instructor: N. Christopher Phillips
The material can be modified depending on the interests of the students.
The Cuntz semigroup of a C*-algebra is a refinement of the semigroup from which the K_0-group is derived. It contains much more information, but is correspondingly harder to study. We introduce and study this semigroup, along with related concepts such as strict comparison of positive elements and the radius of comparison of a C*-algebra; these play an important role in the Elliott classification program. Time permitting, we will examine some of what is known about the Cuntz semigroups of crossed product C*-algebras. As in Math 685, there will be many pointers to other interesting material not actually in the course.
There will be no exams in this course.
Math 690 Morse Theory
Fall 2023
Instructor: Daniel Dugger
Morse theory is a method for understanding the topology of a space by studying the critical points of smooth functions. It is a fundamental collection of techniques that are used in both algebraic and geometric topology, as well as overlapping fields like geometry and combinatorics. This course will be a general introduction to the subject. In addition to covering the foundations we will discuss Morse-Bott theory and the applications to Bott periodicity, Morse homology, and some discrete Morse theory. Students will be assumed to have a basic familiarity with singular homology and homotopy theory, as for example covered in our Math 634-635-636 sequence.
Math 692; Introduction to low-dimensional topology
Spring 2024
Instructor: Robert Lipshitz
This course is intended to serve as an introduction to the techniques and questions in the topology of surfaces, 3-manifolds, and 4-manifolds. We will start with basic results about the mapping class groups of surfaces and use these to study the topology of closed 3-manifolds via Heegaard splittings and Dehn surgery. We will then briefly discuss Kirby calculus for 4-manifolds and geometric structures on 3-manifolds. The course should be accessible to students who have taken 634 and 635.